Answer to Question #250564 in Physics for Rand

Question

Starting from rest, a car accelerated for 4.0 seconds with an acceleration a. It continued for an additional 12.0 seconds with an acceleration a/2, reaching a final speed of 20 m/s. How far did the car travel in the total time of 16 seconds?

Answer 1

Find the speed in 4 s:

$$v_0=at_1.$$

Find the speed in 12 s (after the 4 seconds):

$$v=v_0+\frac a2t_2=at_1+\frac a2t_2=\\\space\\=a\bigg(t_1+\frac {t_2}2\bigg).$$

Hence, find the acceleration:

$$a=\frac{2v}{2t_1+t_2}=2\text{ m/s}^2.$$